Example of iPID controller in Matlab M.file by Michel Fliess?

Hi everyone, I am a masters student at the university of Disburg-Essen. I want to program an iPID controller as proposed by Michel Fliess in his research paper https://arxiv.org/pdf/1305.7085.pdf. As I am still new to Matlab I need a little help to get started. Can anyone who has done the iPID agorithm in a matlab mfile please send it to me? It would help me a lot. Thank you.

[John Masse]

Hi, you can see https://www.researchgate.net/publication/321918636_RelaxC_Controller_The_Ultimate_controller_The_origin It is another point of view which can help you to understand all this stuff.

[islam dib]

Did you find eny solution ?

Answer 1

[Vibhav Gaur]

I am using the iPID algorithm for my thesis project. To get more familiar with it I practiced with a DC motor model. I've done everything in Simulink, but it should still be helpful in understanding how the implementation works.

I have attached my Simulink model and the initialization script so it should run directly out of the box. The initialization script is pre-computing the trapezoidal integration coefficients from the polynomial. Hope this helps!

[SEHILI Laid]

Thank so much bro for this support,

I would like just to ask you about the equations that you have used to simulate this model ! if possible !

[SEHILI Laid]

there is one missing file AlgDerEst.File.m

[Vibhav Gaur]

@SEHILI Laid, I have attached both the required files in the answer above. If you put both the files in the current workspace, the simulation should run. Also, for the equations used in the simulation, please refer to https://www.teses.usp.br/teses/disponiveis/3/3139/tde-27062016-153343/publico/MatheusSchwalbMoraesCorr16.pdf

[SEHILI Laid]

Vibhav Gaur

Please look at pictures below:

The constant (N) and (Phat) are not defined in AlgDerEst_Init.m

also in the script AlgDerEst_Init.m there is one line asks to load the file AlgDerEst_File.mat

that's why your program is not working with me !

I hope you can fix this issue

Regards,

[Vibhav Gaur]

Ahh, sorry about that. I forgot to upload the file where those variables are. Here it is now. Sorry for the delay.

You can uncomment the last two lines to generate the variables and save them in a file called AlgDerEst_File.mat. Or you may handle it any other way you like.

Best,

Vibhav

[SEHILI Laid]

Vibhav Gaur

thank you so much. I sincerely appreciate your generosity.

[Vibhav Gaur]

Glad to be able to help! Good luck

[islam dib]

Hello,

Please, Can you give us equations and how to get command ?

[Joaquín López]

thank you so much Vibhav.

I am starting to work with Model Free Controllers and I think your idea of playing with a motor control in simulink to understand the basics is very good. I think the implementation you propose is quite clear but I do not understand one part of the implementation of Phi in the controller. I would appreciate if you can help me with that. In the image bellow you can see your controller and in a red rectangle the part that I think corresponds to Phi. I have also added the equation of Phi. The first part in the solid blue rectangle corresponds to the first term of the Phi equation and It is very clear for me. The second part in dashed green It seems that does not correspond to the equation. Can you explain why did you change it?. How did you get to that implementation?

Again, thanks a lot for sharing this.

[Joaquín López]

Sorry, the image was too big. I attached it again with a smaller size.

[David]

Joaquin and Vibhav, I understand how you get the blue box, but I don't understand how you get the green box to be this integral. What I see is u(t-1) multiplied by a constant.

[Reurison]

David,

I downloaded the same file and from what I saw in this simulation they are using the ultra-local model of order v = 2, which can be described as y^(2)(t) = Phi(t) + alpha*u(t), so the estimation of Phi(t) is : Phi(t) = y^(2)(t) - alpha*u(t).

As my objective right now it is not to explain the theory behind it, I'll simply put that are "two ways" to estimate Phi(t) (please read the already mentioned work for more details). The first one is to use the expression inside the red box (Eq. 4.13) to directly estimate Phi(t). The other way is only estimate y^(2) using the equations (2.24, 2.39 or 2.49), and doing Phi(t) = estimate_of_y^(2) - alpha*u(t-1) .

Back to the file AlgDerEst.m one can see:

 %Phat(i) = alphak *( (120/T^6) * (4*T^3 - 45*T^2*tau_k(i) + 108*T*tau_k(i)^2 - 70*tau_k(i)^3) );
 Phat(i) = alphak *( (60/T^5) * (T^2 - 6*T*tau_k(i) + 6*tau_k(i)^2) );

Which means that the equation inside the blue box is the equation (2.39) (usind the second way explained above) and the green box as you already mentioned (correctly) is alpha*u(t-1), and not the term mentioned by Joaquín Lopez. It would be necessary to modify the simulink file in order implement what is being shown in the figures above.

Answer 2

[John Masse]

Hi,

I don't have the solution for you. But if you want to create an algebraic filter, try making one outside of the loop control. and apply it on a signal (sinusoid) to check your algorithm. ( use a reverse integrator scheme)

in a control loop you can use a simple numerical derivative to compute y' (Euler is your friend)

after it is complicated because there is no rule, but you have to filter something: the estimation of F or the new U* = (y'* -F(est))/alpha , it is necessary for stabilize the closed loop with a small time constant but not too large ( it is the problem of free model).

But you have to know that ipid works "well" on a process without dead time or gap time. if you want to create a drone it is "ok" but the tuning is empirical, for the rest change of method.

the last advice dont use ki and kd because it is in "redondance"( french word) with the recurence equation of your control ( it is my point of view) .

Good luck and think Relaxc ( the last generation control loop process)